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Determine whether the set with the definition of addition of vectors and scalar multiplication is a...

Determine whether the set with the definition of addition of vectors and scalar multiplication is a vector space. If it is, demonstrate algebraically that it satisfies the 8 vector axioms. If it's not, identify and show algebraically every axioms which is violated. Assume the usual addition and scalar multiplication if it's not defined. V = R^2 , < X1 , X2 > + < Y1 , Y2 > = < X1 + X2 , Y1 +Y2> c< X1 , X2 > = < cX1 , cX2 >

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